Which of the following are the coordinates of a rectangle with a length of 5 units and width of 2 units in the coordinate plane? $$ \begin{array}{l}O(-2,-4),(-2,-2),(2,-4),(2,-2) \ (1,4),(-4,4),(1,6),(-4,6) \ O \ (-3,-0),(-7,-2),(-3,-2),(-7,0) \ (6,-3),(1,0),(6,0)\end{array} $$

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To determine which of the given sets of coordinates represent a rectangle with a length of 5 units and a width of 2 units, we need to check the distances between the points in each set.

1. **Set 1: $$ O(-2,-4),(-2,-2),(2,-4),(2,-2) $$**

- The points are:
     - $$ A(-2, -4) $$
     - $$ B(-2, -2) $$
     - $$ C(2, -4) $$
     - $$ D(2, -2) $$

- Length (horizontal distance between $$ A $$ and $$ C $$):
     $$
     |2 - (-2)| = 4 \text{ units}
     $$
   - Width (vertical distance between $$ A $$ and $$ B $$):
     $$
     |-2 - (-4)| = 2 \text{ units}
     $$
   - This set does not have the correct length.

2. **Set 2: $$ (1,4),(-4,4),(1,6),(-4,6) $$**

- The points are:
     - $$ A(1, 4) $$
     - $$ B(-4, 4) $$
     - $$ C(1, 6) $$
     - $$ D(-4, 6) $$

- Length (horizontal distance between $$ A $$ and $$ B $$):
     $$
     |-4 - 1| = 5 \text{ units}
     $$
   - Width (vertical distance between $$ A $$ and $$ C $$):
     $$
     |6 - 4| = 2 \text{ units}
     $$
   - This set has the correct dimensions.

3. **Set 3: $$ O(-3,-0),(-7,-2),(-3,-2),(-7,0) $$**

- The points are:
     - $$ A(-3, 0) $$
     - $$ B(-7, -2) $$
     - $$ C(-3, -2) $$
     - $$ D(-7, 0) $$

- Length (horizontal distance between $$ A $$ and $$ D $$):
     $$
     |-7 - (-3)| = 4 \text{ units}
     $$
   - Width (vertical distance between $$ A $$ and $$ C $$):
     $$
     |-2 - 0| = 2 \text{ units}
     $$
   - This set does not have the correct length.

4. **Set 4: $$ (6,-3),(1,0),(6,0) $$**

- The points are:
     - $$ A(6, -3) $$
     - $$ B(1, 0) $$
     - $$ C(6, 0) $$

- This set only has three points, so it cannot form a rectangle.

Based on the analysis, the only set of coordinates that represents a rectangle with a length of 5 units and a width of 2 units is:

**Set 2: $$ (1,4),(-4,4),(1,6),(-4,6) $$**.
Set 2: $$ (1,4),(-4,4),(1,6),(-4,6) $$

Which of the following are the coordinates of a rectangle with a length of 5 units and width of 2 units in the coordinate plane? \( \begin{array}{l}O(-2,-4),(-2,-2),(2,-4),(2,-2) \\ (1,4),(-4,4),(1,6),(-4,6) \\ O \\ (-3,-0),(-7,-2),(-3,-2),(-7,0) \\ (6,-3),(1,0),(6,0)\end{array} \)

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